Hillerbee is correct your FAA license issued on the basis of the JAA is only valid if you have a current and valid JAA type rating on the type you intend to fly.
Thank your guys!
You also need to comply with the requirements of SFAR No73 to Part 61 if you are going to fly a R22 or R44 under your FAA license.
It seems to me that it's better to forget about flying the R-22 overthere

If you have the R-22 TR in your JAA license, do awareness training (or manufacturer's safety course) and annual flight rewiev by a FAA CFI requirements still apply?
To get a FAA PPL(H) you need to sit a written (computer) exam, and do at least three hours of training with a FAA CFI(H), then you 'might' (depends on your skill level, an instructor won't sign you off if it's marginal, because if you fail his pass-rate will be down, and can get the instructor in trouble) get an endorsment for the checkride, which you take with a DPE, after that you will have a temporary license issued on the spot. Furthermore you'll need TSA clearance which is not to hard to get, but takes a bit of time.
www.flightschoolcandidates.gov
Is there the same procedure for a FAA CPL(H)?
If someone already has a FAA PPL(H) issued on the basis of the JAA CPL(H) does he still has to take a written exam prior to familiarization flying part and checkride?